A detailed look at electrical equivalents of uniform electrochemical diffusion using nonuniform resistance–capacitance ladders

This paper discusses equivalent-circuit modeling of the electrochemical impedance corresponding to one-dimensional diffusion in a uniform medium. It argues that, of the several equivalent circuits in use for such modeling, one – namely the nonuniform resistance–capacitance ladder – has attractive properties that are not shared by any other equivalent circuit. Explicit, analytical expressions are derived for the efficient development of this ladder equivalent, which provide advantages compared to computer optimization. Although the context of this work is battery modeling, the results presented can be of value in other fields where diffusion is studied and modeled.